We highlight that this martingale representation greatly simplifies the adversary's optimization problem and is only available in a continuous-time setting.
In the discrete-time setting investigated in [1]}, [2]}, [3]}, [4]}, for example, the adversary in each period needs to solve a much more complicated optimization that may involve many decision variables (if there are \(n\)  possible random outcomes at a state, the quantile value allocation problem involves \(n-1\)  real-valued decision variables).
It may not easy in such cases to solve the adversary's optimization problem even numerically.
